The present invention relates to a method for evaluating the phase relations of periodic brightness patterns, several of which are displaced relative to each other and are recorded by means of a camera. During one step, the phase relations of the patterns are determined separately for each individual image point corresponding to individual object points of the individual video images, and then the phase shift of the patterns is determined relative to an initial phase relation.
A way to do this has been suggested in U.S. Pat. No. 4,768,881, where two interferograms are recorded and their strip-like brightness patterns are shifted in phase relative to each other, and hence relative to the camera, by any fraction of a strip, i.e, .alpha.&lt;.pi.. Spatial Fourier transformations are then used to compute--based on each recorded interferogram--the phase values associated with the object points and the phase shift between the two interferograms (evaluation in the spatial domain). The computed phase shift is used only to clearly determine the integral multiple of the number 2 .pi. of the computed phase values, i.e., the so-called phase unwrapping. In so doing, only the sign of the computed phase shift at the object point concerned is considered, while the value of the phase shift remains of no consequence during further evaluation.
A disadvantage of this method is the requirement that a phase shift smaller than .pi. must be established between the two recorded interferograms. Such a small phase shift can easily be caused by vibrations that can occur, for example, when the interferometer is used in a workshop. Then a reliable evaluation of the interferograms is no longer assured.
In addition, this method has the disadvantage that the phase value to be computed for one object point does not remain unaffected by the phase values of adjacent object points on account of the spatial Fourier transformation. The lateral measured resolution, i.e., the resolution in the camera image plane, therefore is lower than the lateral resolution of the camera position itself. This disadvantage exists for all analytical methods that consider the measured values in adjacent object points in addition to that measured in one object point for the computation of the phase value, because the spatial evaluation always acts as a low-pass filter.
The last-mentioned disadvantage has been eliminated in so-called phase displacement methods, where at least three phase-displaced brightness patterns are recorded sequentially and the phase value associated with one object point is computed from the brightness values of the phase-displaced brightness patterns in that object point (evaluation in the time domain). A few algorithms for analyzing such phase-displaced patterns are described in an article by K. Creath, "Comparison of phase measurement algorithms", Proceedings of the SPIE, Vol. 680 (1986).
Phase displacement methods also require that the values of the phase shifts between the patterns be very well known, because the accuracy of these values substantially determines the attainable measurement accuracy. To set the phase shifts precisely, the phase steps may be measured individually or a piezo-translator used for phase displacement may be calibrated accordingly. The Creath article also reveals that four phase-displaced brightness patterns permit the computation of the measured value of a phase shift, provided the phase displacement is always maintained at the same value.
Furthermore, Applied Optics, Vol. 27, 5082 (1988), discloses an iterative method for correcting individual phase steps when a phase displacement method is used. In this case the measured values of sequentially recorded interferograms are evaluated relative to two camera pixels that are in phase quadrature. Based on these measured values, a correction value for the voltage on a piezo-translator used for phase displacement is determined iteratively. The voltage on the piezo-translator is set so that the sum of all phase steps just result in 2 .pi. and the individual phase steps are equidistant.
An improved correction of the phase steps results when the computation of the correction value takes into consideration the measured values of several camera pixels. Upon having computed a correction value for two camera pixels in phase quadrature, the next correction values for the two adjacent camera pixels and then another correction value for the two camera pixels thereafter are computed. This procedure is repeated over an integral multiple of the fringe period. Such an improved correction value represents the mean value based on the individual correction values. In conjunction with this, however, it is again required that the two adjacent camera pixels be in phase quadrature, i.e., that the strip patterns have a spatial frequency relationship that changes only slightly, even over a plurality of camera pixels.
As explained above, all phase displacement methods require that the given phase steps be maintained with high accuracy and that the actual phase steps be accurately determined. Frequently, however, it is not possible to maintain the required accuracy of the phase steps because of the presence of vibrations, requiring complex mechanical damping measures. In this case even corrective measures, such as the highly complex ones described in Applied Optics, Vol. 27, 5082 (1988), fail because the piezo-translator is corrected before the actual topographic measurement is made. The measurement of the actual phase steps is made very complex because the phase steps must be measured with a degree of accuracy that corresponds to the desired measuring resolution of the interferometer.
The problems explained above occur not only in the evaluation of interferometric fringe images but also in the evaluation of topographic measurements using projected moire stripes. Corresponding methods of evaluating moire fringes are suggested in SPIE, vol. 728, 189 (1986), and in U.S. Pat. Nos. 4,488,172; 4,499,492; and 4,641,972. By these methods several stripe patterns with shifted phases are projected on the surface to be evaluated and an image of the projected pattern is recorded. Analogous to phase shift interferometry, the measured intensity values of the different images with shifted phases are used to reconstruct the surface topography at each image point of the camera. This also requires that the values of the phase steps be determined with high accuracy because erroneous phase steps result in erroneous measured values.